=== Twisted cubic parametrization ===
q1∘nu_3 = 0
q2∘nu_3 = 0
q3∘nu_3 = 0

=== Quadratic-generator independence ===
rank(span{q1,q2,q3}) = 3

=== Surface containment ===
f∘nu_3 = 0

=== Homogeneity ===
monomial total degrees = [4]

=== Determinantal reconstruction ===
All three generators are the 2x2 minors of the Hankel matrix.

=== Smoothness of quartic surface ===
chart x=1: gradient ideal is unit = True
chart y=1: gradient ideal is unit = True
chart z=1: gradient ideal is unit = True
chart w=1: gradient ideal is unit = True

PASS: no nonzero projective common zero of the gradient.
PASS: X is smooth over Q (hence over C).

=== Closed-loop theorem bridge ===
Literature theorem (not recomputed here): for a twisted cubic T in a smooth quartic surface X, I_{alpha(T,X),2} = I_{T,2}; the three quadrics cut out T scheme-theoretically.

ALL SYMBOLIC CHECKS PASSED.
Spreadsheet runtime warmup failed during python startup
Traceback (most recent call last):
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/patches/warm_spreadsheet_runtime_on_startup.py", line 26, in warm_spreadsheet_runtime_on_startup
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/spreadsheet_warmup.py", line 785, in warm_spreadsheet_runtime
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/spreadsheet_warmup.py", line 720, in _warm_feature_flows
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/spreadsheet_warmup.py", line 704, in _warm_collaboration_flows
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/generated/interface/models.py", line 32317, in hydrate_crdt_from_proto
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/rpc/remote.py", line 749, in __call__
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/rpc/client.py", line 150, in call
artifact_tool.rpc.client.RemoteError: hydrateCrdtFromProto requires an empty collaborative document.
